Holomorphic functions and polynomial ideals on Banach spaces

Autores
Carando, Daniel Germán; Dimant, Veronica Isabel; Muro, Luis Santiago Miguel
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given A a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, HbA(E). We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum MbA(E) of this algebra “behaves” like the classical case of Mb(E) (the spectrum of Hb(E), the algebra of bounded type holomorphic functions). More precisely, we prove that MbA(E) can be endowed with a structure of Riemann domain over E and that the extension of each f ∈ HbA(E) to the spectrum is an A-holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dimant, Veronica Isabel. Universidad de San Andres. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Muro, Luis Santiago Miguel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Polynomial Ideals
Holomorphic Functions
Riemann Domains Over Banach Spaces
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/17535
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Holomorphic functions and polynomial ideals on Banach spacesCarando, Daniel GermánDimant, Veronica IsabelMuro, Luis Santiago MiguelPolynomial IdealsHolomorphic FunctionsRiemann Domains Over Banach Spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given A a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, HbA(E). We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum MbA(E) of this algebra “behaves” like the classical case of Mb(E) (the spectrum of Hb(E), the algebra of bounded type holomorphic functions). More precisely, we prove that MbA(E) can be endowed with a structure of Riemann domain over E and that the extension of each f ∈ HbA(E) to the spectrum is an A-holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras.Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dimant, Veronica Isabel. Universidad de San Andres. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Muro, Luis Santiago Miguel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2010-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/17535Carando, Daniel Germán; Dimant, Veronica Isabel; Muro, Luis Santiago Miguel; Holomorphic functions and polynomial ideals on Banach spaces; Springer; Collectanea Mathematica; 73; 1; 1-2010; 71-910010-07572038-4815enginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s13348-010-0025-5info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs13348-010-0025-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:47:17Zoai:ri.conicet.gov.ar:11336/17535instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:47:17.549CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Holomorphic functions and polynomial ideals on Banach spaces
title Holomorphic functions and polynomial ideals on Banach spaces
spellingShingle Holomorphic functions and polynomial ideals on Banach spaces
Carando, Daniel Germán
Polynomial Ideals
Holomorphic Functions
Riemann Domains Over Banach Spaces
title_short Holomorphic functions and polynomial ideals on Banach spaces
title_full Holomorphic functions and polynomial ideals on Banach spaces
title_fullStr Holomorphic functions and polynomial ideals on Banach spaces
title_full_unstemmed Holomorphic functions and polynomial ideals on Banach spaces
title_sort Holomorphic functions and polynomial ideals on Banach spaces
dc.creator.none.fl_str_mv Carando, Daniel Germán
Dimant, Veronica Isabel
Muro, Luis Santiago Miguel
author Carando, Daniel Germán
author_facet Carando, Daniel Germán
Dimant, Veronica Isabel
Muro, Luis Santiago Miguel
author_role author
author2 Dimant, Veronica Isabel
Muro, Luis Santiago Miguel
author2_role author
author
dc.subject.none.fl_str_mv Polynomial Ideals
Holomorphic Functions
Riemann Domains Over Banach Spaces
topic Polynomial Ideals
Holomorphic Functions
Riemann Domains Over Banach Spaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given A a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, HbA(E). We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum MbA(E) of this algebra “behaves” like the classical case of Mb(E) (the spectrum of Hb(E), the algebra of bounded type holomorphic functions). More precisely, we prove that MbA(E) can be endowed with a structure of Riemann domain over E and that the extension of each f ∈ HbA(E) to the spectrum is an A-holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras.
Fil: Carando, Daniel Germán. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dimant, Veronica Isabel. Universidad de San Andres. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Muro, Luis Santiago Miguel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Given A a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type, HbA(E). We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum MbA(E) of this algebra “behaves” like the classical case of Mb(E) (the spectrum of Hb(E), the algebra of bounded type holomorphic functions). More precisely, we prove that MbA(E) can be endowed with a structure of Riemann domain over E and that the extension of each f ∈ HbA(E) to the spectrum is an A-holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras.
publishDate 2010
dc.date.none.fl_str_mv 2010-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/17535
Carando, Daniel Germán; Dimant, Veronica Isabel; Muro, Luis Santiago Miguel; Holomorphic functions and polynomial ideals on Banach spaces; Springer; Collectanea Mathematica; 73; 1; 1-2010; 71-91
0010-0757
2038-4815
url http://hdl.handle.net/11336/17535
identifier_str_mv Carando, Daniel Germán; Dimant, Veronica Isabel; Muro, Luis Santiago Miguel; Holomorphic functions and polynomial ideals on Banach spaces; Springer; Collectanea Mathematica; 73; 1; 1-2010; 71-91
0010-0757
2038-4815
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s13348-010-0025-5
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs13348-010-0025-5
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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